1   Introduction

Due to the low fuel consumption and high torque output, diesel engines, as an important part of traditional power, are widely used in non-road machinery. With the increasingly stringent emission regulations, diesel engines are required to be upgraded and improved (Wang et al. 2021; Georgiou and Azimov 2020; Tadros et al. 2020; Liu et al. 2018; Song et al. 2013). Accordingly, the Chinese government implemented the third stage of emission regulations for non-road diesel engines in October, 2014. In fact, NO_x emissions need to be decreased by 30%‒45% form the second-stage emission regulations. Due to its potential of reducing NO_x emissions, the Miller cycle, as an in-engine purification, has become a research hotspot (Gonca et al. 2015; Luo and Sun 2016; Benajes et al. 2014; Liu et al. 2016).

In recent years, numerous research works have been conducted to improve engine performance using the Miller cycle. Moreover, the engine design through the Miller cycle has been optimized to reduce NO_x emissions (Zerom and Gonca 2020; Liu et al. 2016; Cui et al. 2014) and improve fuel economy (Li et al. 2014; He et al. 2019). Yang et al. (2019) used boost technology to calculate the changes in engine performance and its emissions. Their research shows that an earlier intake valve closing (IVC) will significantly prolong the retardation period. However, the optimization of the ignition strategy can basically maintain the combustion phase stability, whereas delaying the exhaust valve opening (EVO) will increase the residual exhaust rate, slow down the combustion rate, lengthen the combustion duration, and delay the combustion phase. Leng et al. (2014) used a three-dimensional simulation tool to analyze the characteristics of NO_x generation, they investigated that an improved in-cylinder combustion path can avoid the formation of NO_x, so that NO_x emissions can be decreased.

Kyrtatos et al. (2014) investigated an extreme Miller valve timing in a large-bore medium-speed diesel engine and observed that a long ignition delay, due to a low in-cylinder charge temperature, led to great premixed combustion. However, beyond that, the long ignition delay further let the spray penetrate, enhancing the air entrainment and resulting in an overall leaner premixed combustion, which would accelerate NO_x formation. This process can also result in unstable combustion and high cycle-to-cycle variation of the in-cylinder pressure, which can affect the engine performance. Imperato et al. (2016) realized that the Miller cycle is a well-known approach for meeting emission legislation for sea-going vessels, which can reduce the in-cylinder temperature prior to combustion. They tested the first systematic study on split injection combined with the Miller cycle in large-bore engines, and observed that the pilot injection reduced the ignition delay but dropped the peak of the premixed combustion only when the most advanced intake valve was closing. This technology improved the fuel economy but provided no advantages when emissions were concerned. In addition, increasing the injection dwell reduced NO_x emissions, and increased fuel consumption. The highest NO_x reduction was close to 60%, with a small drawback in fuel economy. Feng et al. (2016) conducted a simulation study on a low-speed two-stroke marine diesel engine. Its speed was 142 r/min and the output power was 3 575 kW. With the original intake flow rate, a 10% exhaust gas recirculation (EGR) rate and medium Miller cycle reduced the NO_x emission by 56% and had no increased specific fuel consumption penalties compared to the original engine. When the EGR rate was 20%, the emission reduction of NO_x reached 77%, but with a considerably high price increase of the specific fuel consumption.

In this study, the Miller cycle was applied to a medium-speed turbocharged diesel engine, and relevant experiments were performed. The diesel engine model was established by AVL BOOST. Based on the verification of the numerical model, the influencing factors of the performance and NO_x emissions with the Miller cycle were explored, and the results show that they satisfied the third-stage regulations. Furthermore, the Miller cycle will be a reference to improve the design of non-road diesel engines.

2   One-dimensional BOOST calculation model and scheme

2.1   Miller cycle principle

The Miller cycle changes the intake valve timing such that the actual compression ratio of the intake stroke becomes less than that of the exhaust stroke, which controls the intake air mass and temperature of the compression top dead center (TDC). Two schemes are considered in the application of the Miller cycle (Zhao 2017; Zhu et al. 2017; Dobrucali 2016; Li et al. 2019): early intake valve closure (EIVC) and late intake valve closure (LIVC). Compared with the LIVC, the EIVC has a shorter intake stroke, which is less likely to intake the backflow, so the heat transfer loss of the EIVC is lower. In addition, the exhaust pressure of the EIVC is higher, which is conducive for better exhaustion, and the pumping loss is relatively lower than that of the LIVC. Accordingly, this paper focuses on the EIVC. Figure 1 shows the relationship between the temperature and volume of the in-cylinder in the Miller cycle (1 → 1e → 2 → 3 → 4 → 5 → 1e) and the standard cycle (1' → 2' → 3' → 4' → 5' → 1'). The Miller cycle starts from IVC at point 1 before the BDC during the intake stroke, which leads to the intake valve's early closure. The in-cylinder working medium undergoes an adiabatic expansion process (1 → 1e), and then begins the adiabatic compression process (1e → 2). The effective compression stroke is shorter than the adiabatic compression stroke (1' → 2') of the standard cycle, so the effective compression ratio (ECR) of the Miller cycle becomes smaller. The in-cylinder temperature T₂ of Miller cycle is lower than that of the standard cycle T_2' at the end of the compression. Therefore, the maximum combustion temperature T₄ is lower than that of T_4'. For a naturally-aspirated engine with the Miller cycle, compared to the intake air flow of the original engine, the cycle will be reduced because the intake stroke is shorter. The reduction of the intake air mass has a negative effect on the combustion and output power of the engine. Therefore, in order to an ensure adequate intake of air mass, the supercharging technology should be adopted to reduce the combustion temperature, and ensure a high power output of diesel engines (Zamboni et al. 2016; Gonca and Sahin 2017).

Figure  1  Temperature (T)-volume (V) diagram for the Miller cycle and standard cycle

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2.2   Numerical simulation

2.2.1   Experimental setup and BOOST model

The experiments were performed using a four-stroke, six-cylinder turbocharged direct injection diesel engine. The engine is a 6PC2-6/2L marine diesel engine produced by Shaanxi Diesel Heavy Industry Co., Ltd, Xianyang, China. The number of valves is four, the shape of the combustion chamber is a shallow basin, and the injector is in a central position. The main parameters of the engine are listed in Table 1.

The AVL BOOST software has a rich library of components, and it simplifies a complex engine into different sub-modules such as an intake system, cylinder system, and exhaust system. Based on the structural parameters and technical specifications of the diesel engine components, the engine model was built, as shown in Figure 2. The model is mainly composed of a system boundary, air cleaner, turbocharger, cooler, intake and exhaust pipes, and cylinders.

Figure  2  Schematic diagram of the BOOST model

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2.2.2   Selection of the combustion model

The AVL mixture controlled combustion (MCC) model was selected. The injection rate and kinetic energy of the fuel injection into the cylinder were calculated using the structural parameters of the input (e. g., the number of holes, nozzle diameter, flow coefficient, etc.). The MCC model was established. Consequently, Dobos and Kirkpatrick (2017), Qi et al. (2011), Lucchini et al. (2017) accurately predicted the heat release rate.

The heat release rate is a function of the combustible fuel mass and the turbulent kinetic energy density:

where Q_MCC is the fuel heat dissipation, α is the crank angle, C_C is the combustion constant, m_f is the mass of the fuel evaporation, k is the local turbulent kinetic energy density, v is the cylinder volume, H_μ is the fuel's low calorific value, w₀ is the mass fraction of oxygen available at the fuel injection start time, C_EGR is the influence of constant of the EGR rate, and C_R is the mixing rate constant.

Because the kinetic energy of the squish and swirl flow is relatively small, the kinetic energy of the in-cylinder fuel is determined by the fuel injection rate:

where E_{K, F} is the kinetic energy of the fuel, V_F is the injection rate, n is the engine speed, μA is the effective orifice area, and ρ_F is the fuel density.

2.3   Model validation

The differences between the simulation and experimental data in terms of the average in-cylinder pressure and NO_x emission are depicted in Figure 3. Four conditions were calculated at the working cycle of the E3 (four kinds of loads, i.e., 100%, 75%, 50%, and 25%, according to marine application propeller law) diesel engine, and the accuracy of the model was verified by comparing the experimental and calculated results. As shown in Figure 3(a), all differences are within the desired 2% limit of the experimental data, and the simulated average in-cylinder pressure is in good agreement with the experimental results of the original engine at four operating conditions. Thus the relative error value of the experimental and simulated data is within a reasonable range.

Figure  3  Comparison of the average in-cylinder pressure and NO_x emissions

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The simulated and experimental NO_x emissions are shown in Figure 3(b), where the maximum error is approximately 7% at 50% and 100% loads, and less than 3% at 25% and 75% loads. This outcome is attributed to the lack of OH during the combustion. Moreover, Eq. (8) in Section 3.3 is neglected, and this model just calculates the thermal NO_x based on the Zeldovich mechanism. Thus, the simulated results have shown a satisfying agreement with the experimental data, and the model can predict the NO_x emissions. The effects of the blow-by, leakage, and cycle-to-cycle variations partially led to the discrepancies (Luo and Sun 2016; Nahim et al. 2015). Due to limited experimental conditions, a few initial and boundary parameters adopt the empirical value. The speed, boost ratio, heat load variations, initial conditions, boundary conditions, and characteristics of the spray and combustion are quite different at different loads in the E3 cycle. Furthermore, the simulation results are in line with the in-cylinder combustion and NO_x emissions of the diesel engine, which indicates that the establishment of the model is reliable, and the parameters of the simulation model are accurate.

2.4   Miller cycle solutions

This study focuses on the EIVC. Seven different intake cam profiles were designed for the target diesel engine. In this process, the intake duration and valve lift were adjusted when the valve opening time stayed unchanged. The adjusted valve lift curve is shown in Figure 4. In the original engine, the valve closure time is 220 crank angle degrees (CAD). Seven kinds of schemes could be created by advancing the IVC time, i. e., 180 CAD (TDC), 170 CAD, 160 CAD, 150 CAD, 140 CAD, 130 CAD, 120 CAD, which are abbreviated as IVC180, IVC170, IVC160, IVC150, IVC140, IVC130, and IVC120, respectively. The new intake valve lift curve was imported into the BOOST model, and then the performance of the diesel engine with the Miller cycle was studied by calculating the scheme of the E3 cycle at four loads.

Figure  4  Valve lift curve of different Miller cycles

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2.5   Simulation results and analysis of the Miller cycle

The following conditions should be given more attention. First, to ensure adequate output power, the intake air volume should be the same as that in the original engine. Moreover, the cooler should be adjusted to maintain the temperature of the working medium after turbocharging. Figure 5 shows the change in the ECR's different Miller cycle schemes.

Figure  5  Effective compression ratio of different Miller cycles

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The definition of the ECR is given as:

As indicated in Eq. (5), the ECR is defined as the ratio of the in-cylinder volume at the IVC timing (V_IVC) to the volume at the TDC (V_TDC).

When the IVC timing reached the maximum and the compression ratio at the TDC was 11.4, the effective compression stroke became shorter, and the ECR gradually decreased with the increase in the advance angle. When the IVC was 120 CAD, the ECR was 9.27.

Figure 6 shows the changes in the boost pressure under different Miller cycles. The higher the load was, the higher the boost pressure was. At the same load, the boost pressure gradually increased with the EIVC. The boost pressure moderately changed at medium and low loads, but it rose faster at a high load. At 100% load, the boost pressure reached 5.62 bar with IVC120. Generally, when the boost pressure exceeded 5 bar, the single-stage turbocharging cannot meet the requirements, so the two-stage turbocharging was used. Figure 7 shows the changes in the in-cylinder residual exhaust gas volume with different Miller cycles. The in-cylinder residual exhaust gas coefficient was almost consistent at medium and low loads. However, at high load, the in-cylinder residual exhaust gas sharply increased when the IVC was earlier. Moreover, because the intake pressure was very high at this time, and the high intake pressure prevented the exhaust gas with low pressure in the cylinder from discharging, the residual exhaust gas increased.

Figure  6  Boost pressure of different Miller cycles

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Figure  7  Residual exhaust gas coefficient of different Miller cycles

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Figure 8 shows the comparison of the in-cylinder pressure and temperature with different Miller cycles when the intake valve was closed in the original engine. The trends of the temperatures and pressures were the same under different working conditions, and they all decreased the increases in the EIVC. With the downward movement of the piston, the temperature and pressure of the working medium both dropped. The earlier the IVC appeared, the longer the expansion process continued, and the lower the temperature was. The IVC temperature of the original engine decreased by approximately 5 K, when IVC advanced by 10 CAD. Based on the gas state conservation equation, the total intake air volume was constant. The lower the temperature, the lower the pressure.

Figure  8  Comparison of the in-cylinder pressure and temperature of different Miller cycles

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Figure 9 shows the changes in the specific fuel consumption with different Miller cycles. The specific fuel consumption was almost unchanged with the increase in the EIVC, Particularly, the specific fuel consumption began to increase only at the IVC130 and IVC120. The intake air temperature was too low because the fuel and air mixture was not mixed evenly, resulting in low combustion efficiency and high fuel consumption.

Figure  9  Fuel consumption at different Miller cycles

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3   Effects of the Miller cycle on the combustion and NO_x emission at high loads

3.1   Effect of the Miller cycle on the cylinder parameters

Figure 10 shows the calculation results of the in-cylinder pressure with different Miller cycles. The in-cylinder temperature was different at 220 CAD under different Miller cycles. The schemes were analyzed, and the results show that the initial in-cylinder temperature difference was approximately 10 K at the following points: IVC180, IVC160, IVC150, IVC140, IVC130, and IVC120. The in-cylinder pressure decreased with the EIVC during the compression phase. The intake air volume stayed unchanged, so the intake air temperature and intake air pressure were reduced. During the combustion stage, the rate of the pressure rise increased with the advancement of the IVC time, and the moment of the rapid increase in the in-cylinder pressure also lagged behind, especially at 75% load. The cylinder peak pressure decreased with the advancing angle of the IVC from IVC180 to IVC130 at 100% load. However, they began to rise at IVC120. At 75% load, the IVC130 and IVC120 schemes showed that the peak pressures were higher than that of the original engine. The in-cylinder temperature dropped with the increase in the Miller cycle degree during the injection, followed by the declining in-cylinder pressure in the compression stage. To keep the excess air coefficient constant, the initial pressure would be reduced proportionately in the combustion stage with the decrease in the initial temperature, and the phase of the in-cylinder pressure increasing rapidly would be delayed. The reason was that the ignition delay increased with the decrease in the in-cylinder temperature during the injection time. More combustible mixture was formed in the longer ignition delay period, resulting in the increase in the heat release rate during the premixed combustion stage, and the in-cylinder pressure increased. Therefore, the difference of the six curves was highly evident in the compression stage, and then, they reached the same or higher explosive pressure than the original machine in the combustion stage. Moreover, all the pressure curves gradually coincided in the expansion stage.

Figure  10  Effects of different Miller cycles on the in-cylinder pressure

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Figure 11 indicates the average in-cylinder temperature for different Miller cycles. The average in-cylinder temperature of the compression stage gradually decreased with the initial charge temperature reduction. Meanwhile, the starting moment of the average temperature increase was delayed. In most Miller cycle schemes, the average in-cylinder temperature was nearly the same as of the original engine after it rapidly increased, and the rise of the average in-cylinder temperature at 75% load was more evident and faster than that of the 100% load. The curves of both loads almost coincided with that of the original engine, and their trends were the same. At the same time, the peaks of the average temperature were closer. Except for the IVC130, and IVC120 at 75% load, the initial charge temperature was reducing with the advancement of the IVC, making more combustible mixture to be formed in a longer ignition delay period, and the combustion drastically accelerated. In addition, the maximum average in-cylinder temperature rise rate increased, and the peak value was higher than that of the original engine.

Figure  11  Effects of Miller cycles on the average in-cylinder temperature

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3.2   Effect of Miller cycles on the combustion characteristics of the cylinder

Figure 12 represents the calculation results of the in-cylinder temperature of the injection timing and ignition delay period with different Miller cycles. As can be seen, with the IVC from 220 CAD to 120 CAD, the average in-cylinder temperature was reduced by 100 K with a nearly linear decline during the injection at 100% and 75% loads. The temperature of the fuel injection timing and the in-cylinder temperature near the TDC during the compression phase were affected by the Miller cycle. However, the temperature and pressure at the end of the compression were the key factors to the ignition delay period. In fact, the ignition delay period was lengthened. The ignition delay period increased by 1 CAD when the in-cylinder temperature at the time of injection was reduced by 20 K. When the in-cylinder temperature was further reduced, the ignition delay period increased faster, as seen at the IVC120 at 75% load when the ignition delay period sharply increased to 19 CAD. Comparing the curves at 100% load with those at 75% load, the initial intake air temperature at 75% load was lower than that at 100% load. Clearly, at 75% load, the temperature during the injection was lower than that at 100% load, and its ignition delay period was longer. More mixtures were formed during the longer ignition delay period and the premixed combustion was accelerated, so the heat release rate increased.

Figure  12  Effect of Miller cycles on the in-cylinder temperature at the start moment of the injection and ignition delay

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The changes in the heat release rate for different Miller cycles are illustrated in Figure 13. At 100% load, the start stage of the burning was delayed and the peak of the premixed combustion sharply rose with the EIVC. The peak of the diffusion combustion was close to that of the other schemes. At IVC120, the trend of the heat release rate at 75% load was the same as that at 100% load. The heat release rate had only one single peak, and its value was much higher than that of the original engine and twice as high as the IVC130. This effect can be attributed to the temperature at the TDC, which was very close to the ignition limit. When the ignition delay period was increased to 19 CAD, the combustion process was changed. This result highlights that the burning rate was very high and the heat release duration was very short.

Figure  13  Effect of Miller cycles on the heat release rate

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3.3   Effects of Miller cycles on NO_x emissions

The important pollutant in diesel engine is NO_x. NO and NO₂ are grouped together as NO_x. However, NO is the predominant component of NO_x due to the high in-cylinder temperature. The principal reactions of the NO formation based on the extended Zeldovich mechanism are reversible (Muzio and Quartucy 1997; Zeldovich et al. 2014). In the combustion chamber, the thermal NO was generated through the chemical reaction (6) of oxygen atoms and nitrogen molecules and was the major source of the NO in engines which was dependent on the high temperature (above 1 800 K). A part of nitrogen was also found in the mixture, and NO was formed through the nitrogenous organic compounds with oxygen during combustion. Eq. (8) shows the amount of NO formed in the concentrated mixture, which can be neglected as a result of frequent OH inadequacy.

The formation rate of NO was dependent on the reaction temperature, and the reaction rate rapidly increased at high temperatures. By changing the intake valve timing, the maximum temperature in the combustion chamber was reduced, which resulted in NO_x reduction. Generally, the application of Miller cycles causes the effective compression stroke to be shorter than the expansion stroke. In the case of a constant geometric compression ratio, the ECR was thereby reduced and the in-cylinder charge temperature decreased.

The changes of NO mass fraction with different Miller cycles are presented in Figure 14. At 100% load, when the timing of the IVC was changed from 220 CAD to 130 CAD, the NO mass fraction gradually decreased from 1653 × 10^-6 to 1185 × 10^-6. Based on the results, the Miller cycle can effectively reduce NO emissions. When EIVC was 120 CAD, the NO mass fraction was slightly higher than that of the IVC130. At 75% load, the NO mass fraction of the IVC140 was the lowest, i.e., 1850 × 10^-6. However, it rebounded slightly at IVC130. Particularly, the NO mass fraction of IVC120 rapidly increased to 2940 × 10^-6, which was far more than the emission of the original engine at 75% load.

Figure  14  Effect of Miller cycles on NO emissions

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Higher Miller cycle degrees contributed to lower temperatures in the combustion chamber, except for the IVC120 at 75% load. Hence, for diesel engine at medium and high loads, lowering charge temperature by blindly increasing the Miller cycle degree, was not conducive to the reduction of NO_x emissions. In the IVC140 scheme, the Miller cycle degree was further increased after the load exceeded 75%, which lowered the charge temperature. The ignition delay period was too long with low charge temperature, and then the heat release of the premixed combustion sharply increased, prompting the in-cylinder temperature of the diffusion combustion process to rise, and NO_x emissions to increase.

4   Conclusions

To save energy and protect the environment, highly efficient and clean combustion is an important research topic in the marine diesel field. Thus, it is becoming urgent to develop new control technologies on NO_x emission to satisfy the increasingly stringent regulations. Low costs and low fuel consumptions are the primary tasks for the upgrading of existing marine diesel engines. The Miller cycle is an effective method for in-engine NO_x purification due to its moderate reconstruction costs and great reduction of NO_x emissions by nearly constant fuel consumption among others. Based on the discussion of the results obtained, the main conclusions are derived:

1) The diesel engine model was established by BOOST, which was calibrated using test data. The main principles of the Miller cycle and the accuracy of the E3 cycle calculating model were analyzed and validated with experimental results. To calculate the closing time of different intake valves, seven sets of intake cam profiles were designed. The simulation results show that the specific fuel consumption almost had no change, except when the IVC was too early, which slightly increased. At the same time, the intake pressure was very high at the IVC120 at 100% load.

2) The effect on four load conditions with Miller cycles at medium speed was analyzed. The results indicate that the appropriate EIVC can reduce the in-cylinder pressure, temperature and NO emissions. Meanwhile, due to the low temperature during injection, the ignition delay period is lengthened. This condition led to more combustible mixtures, so the premixed combustion was accelerated. When the EIVC was too early, the start stage of burning was seriously delayed and the heat release rate rapidly increased. In fact, the combustion temperature and NO emissions both increased. When the IVC was much too early, the engine could not ignite at low load.

3) The optimal EIVC varies with different loads, and the corresponding best EIVC will increase with increasing loads. At 100% load, IVC130 is the best scheme. When the NO mass fraction is 1 185 × 10^-6, it is 28% lower than that of the original engine. At 75% load, IVC140 is the best scheme. When the NO mass fraction is 1 850 × 10^-6, it becomes 11% lower than that of the original engine.